Angle abc is formed by segments ab and bc on the following coordinate grid: a coordinate grid is shown from positive 6 to negative 6 on the x-axis and from positive 6 to negative 6 on the y-axis. a line segment ab is shown with a as ordered pair 1, negative 1 and b as ordered pair 5, negative 4. another line segment bc is shown with c as ordered pair 1, negative 4. angle abc is rotated 90 degrees counterclockwise about the origin to form angle a'b'c'. which statement shows the measure of angle a'b'c'? a) m∠ a'b'c' = 90 degrees b) m∠ a'b'c' = m∠abc c) m∠ a'b'c' = 180 degrees d) m∠ a'b'c' = 2 ⋅ m∠abc

Option: B is the correct answer.

                B) m∠ A'B'C' = m∠ABC

We are given coordinates of Point A,B and C as:

A(1,-1) , B(5,-4) and C(1,-4)

Since, on rotating the points 90 degree counterclockwise about the origin the rule that holds for this transformation is:

(x,y) → (-y,x)

Hence,

A(1,-1) → A'(1,-1)

B(5,-4) → B'(4,-5)

C(1,-4) → C'(4,-1)

As we know that the rotation is a rigid transformation that is the shape and size of the figure is preserved.

Also, the angle measure remains the same.

                Hence, m∠ABC=m∠A'B'C'

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.

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step-by-step explanation: